GREEN BAY, Wis. -- Another game-winning, fourth-quarter drive made its way into the 49ers' storied playoff history Sunday. But none ever came in this fashion.

Never had they celebrated on a game-ending field goal, which Phil Dawson provided with a 33-yard kick to clinch the 23-20, wild-card triumph over the Green Bay Packers.

And never had the 49ers won a playoff game at the NFL's most sacred stadium. This was only their third such attempt, but that warm-blooded West Coast team just won Lambeau Field's seventh-coldest game ever (5 degrees at kickoff).

"Didn't think we were going to pull it out, did you?" 49ers coach Jim Harbaugh said giddily to open his postgame news conference.

The fifth-seeded 49ers (13-4) indeed kept alive their quest for an elusive sixth Lombardi Trophy. They'll play next Sunday at No. 2-seed Carolina (12-4), a divisional-round game that doubles as a rematch of the Panthers' 10-9 win at Candlestick on Nov. 10.

The 49ers owed much of their win to Kaepernick's fourth-quarter magic. It was a personal hat trick of sorts against his childhood team. He'd tormented Green Bay in last season's playoff opener, this season's regular-season debut and again when it counted Sunday.

Kaepernick used his arm to ignite the winning drive -- throwing completions of 11 and 17 yards to Michael Crabtree -- and used his legs to keep alive that 65-yard, 14-play march over the final 5:06.

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"Colin Kaepernick, we can all agree, is a clutch performer," Harbaugh said. " ... On the time when it matters most, that's what I would call clutch. He's Kaepernick tough. It's pretty awesome."

Kaepernick got the 49ers into field-goal range when he scrambled 11 yards on third-and-8 to the Packers 27.

"I was trying to go to (Crabtree) one-on-one, it didn't look good to me, so I tried to make something happen," Kaepernick said.

It was his seventh and final carry, giving him a team-high 98 rushing yards and his second-most ever behind last year's 181-yard trouncing of the Packers in a 45-31 divisional win.

"We needed a play, and he got it," said Frank Gore, who blocked blitzing cornerback Jarrett Bush to spring Kaepernick.

Gore (20 carries, 66 yards) ate up 12 more yards on the four ensuing snaps to set up Dawson's winner. No run was bigger than his 3-yard conversion on third-and-3, as he followed the blocks of Alex Boone, Anthony Davis, Mike Iupati and Will Tukuafu.

Speaking of close, before Dawson's kick went off the right hash mark and inside the right goal post, replays showed the ball barely sneaking through the outstretched arms of Davon House, who got called offside anyhow.

Harbaugh repeatedly remarked that this wasn't the 49ers' first comeback finish. Only a week earlier, Dawson kicked the game-winner as time expired at Arizona.

As much as Harbaugh adored his quarterback's clutch capacity, Kaepernick nearly became the goat. Three snaps into the final drive, Micah Hyde dropped a potential interception at the 33-yard line, with no one between him and a game-breaking touchdown return.

Kaepernick completed 16 of 30 for 227 yards with one touchdown, and what a timely touchdown it was.

Only 1:35 after the 49ers fell behind 17-13, the 49ers retook the lead when Kaepernick connected with Vernon Davis on a 28-yard pass with 10:31 remaining.

"Kap dropped back, and he just took a chance," Davis said of his seventh touchdown in seven games against Green Bay. "He trusts me."

The Packers wisely entrusted Aaron Rodgers (17 of 26, 177 yards, one touchdown) to work his sack-evading magic in the fourth quarter.

On a play Harbaugh called "spectacular," Rodgers escaping Ray McDonald's grasp and completed a fourth-and-2 pass to Randall Cobb for 26 yards to the 4. Two snaps later, John Kuhn had a 1-yard touchdown plunge to put the Packers ahead 17-13 with 12:06 remaining.

On the Packers' next series, Rodgers avoided blitzing cornerback Perrish Cox and found Cobb again, this time for a 25-yard completion to the 9. But the Packers had to settle for a tying field goal with 5:06 left.

"We did a great job when it counted most," linebacker Patrick Willis said. "Holding them to three (points) was huge."

Settling for field goals is what cost the 49ers two months ago in their 10-9 loss to Carolina.

"This win is a first step to a long road," McDonald said. "Carolina beat us, and we need to come back and hopefully redeem ourselves."